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Chapter 3: Q. 23 (page 174)

Demand Equation The price p (in dollars) and the quantity

x sold of a certain product obey the demand equation

p=-110x+1500鈮�x鈮�1500

(a) Express the revenue R as a function of x.

(b) What is the revenue if 100 units are sold?

(c) What quantity x maximizes revenue? What is the

maximum revenue?

(d) What price should the company charge to maximize

revenue?

Short Answer

Expert verified

(a) R=-110x2+150x

(b) R=14000

(c) x=750&R=56250

(d) To maximize revenue, pricerole="math" localid="1647360230117" =$75

Step by step solution

01

Part (a) Step 1. Given Information

p=-110x+150

02

Part (a) Step 2. Calculation 

R=xp=x(-110x+150)=(-110x2+150x)

03

Part (b) Step 1. Given Information

p=-110x+150

04

Part (b) Step 2. Calculation

For x=100,

R=-110脳10000+150脳100

=14000

05

Part (c) Step 1. Given Information

p=-110x+150

06

Part (c) Step 2. Calculation

To maximize revenue,

R'(x)=-15x+150, which is equal to zero

or,-15x+150=0or,x=750

and maximum revenue isR=56250

07

Part (d) Step 1. Calculation

p=-110x+150

08

Part (d) Step 2. Calculation

To maximize revenue x=750

Then p=-110x+150

or,p=-110脳750+150=75

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Most popular questions from this chapter

In problems 3-6, use the figure to solve each inequality.

a) f(x)>0

b)f(x)鈮�0

In Problems 6鈥� 8, graph each quadratic function using transformations (shifting, compressing, stretching, and/or reflecting).

fx=x-22+2

If G(x)=-2,then

(a) Determine the slope and y-intercept of each function.

(b) Use the slope and y-intercept to graph the linear function.

(c) Determine the average rate of change of each function.

(d) Determine whether the linear function is increasing, decreasing, or constant.

What are the possibilities for the number of times the graphs of two different quadratic functions intersect?

Plot the points (1,5),(2,6),(3,9),(1,12)in the Cartesian plane. Is the relation {(1,5),(2,6),(3,9),(1,12)}a function? Why?

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